Best Known (84, 97, s)-Nets in Base 3
(84, 97, 88573)-Net over F3 — Constructive and digital
Digital (84, 97, 88573)-net over F3, using
- net defined by OOA [i] based on linear OOA(397, 88573, F3, 13, 13) (dual of [(88573, 13), 1151352, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(397, 531439, F3, 13) (dual of [531439, 531342, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(397, 531439, F3, 13) (dual of [531439, 531342, 14]-code), using
(84, 97, 177147)-Net over F3 — Digital
Digital (84, 97, 177147)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(397, 177147, F3, 3, 13) (dual of [(177147, 3), 531344, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using
(84, 97, large)-Net in Base 3 — Upper bound on s
There is no (84, 97, large)-net in base 3, because
- 11 times m-reduction [i] would yield (84, 86, large)-net in base 3, but